Designing open quantum systems with known steady states: Davies generators and beyond

We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ g...

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Main Authors: Jinkang Guo, Oliver Hart, Chi-Fang Chen, Aaron J. Friedman, Andrew Lucas
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2025-01-01
Series:Quantum
Online Access:https://quantum-journal.org/papers/q-2025-01-28-1612/pdf/
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author Jinkang Guo
Oliver Hart
Chi-Fang Chen
Aaron J. Friedman
Andrew Lucas
author_facet Jinkang Guo
Oliver Hart
Chi-Fang Chen
Aaron J. Friedman
Andrew Lucas
author_sort Jinkang Guo
collection DOAJ
description We provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.
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institution Kabale University
issn 2521-327X
language English
publishDate 2025-01-01
publisher Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
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spelling doaj-art-305cb716a63140aeb31369f7f181f02d2025-01-28T10:57:27ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019161210.22331/q-2025-01-28-161210.22331/q-2025-01-28-1612Designing open quantum systems with known steady states: Davies generators and beyondJinkang GuoOliver HartChi-Fang ChenAaron J. FriedmanAndrew LucasWe provide a systematic framework for constructing generic models of nonequilibrium quantum dynamics with a target stationary (mixed) state. Our framework identifies (almost) all combinations of Hamiltonian and dissipative dynamics that relax to a steady state of interest, generalizing the Davies’ generator for dissipative relaxation at finite temperature to nonequilibrium dynamics targeting arbitrary stationary states. We focus on Gibbs states of stabilizer Hamiltonians, identifying local Lindbladians compatible therewith by constraining the rates of dissipative and unitary processes. Moreover, given terms in the Lindbladian not compatible with the target state, our formalism identifies the operations – including syndrome measurements and local feedback – one must apply to correct these errors. Our methods also reveal new models of quantum dynamics: for example, we provide a “measurement-induced phase transition” in which measurable two-point functions exhibit critical (power-law) scaling with distance at a critical ratio of the transverse field and rate of measurement and feedback. Time-reversal symmetry – defined naturally within our formalism – can be broken both in effectively classical and intrinsically quantum ways. Our framework provides a systematic starting point for exploring the landscape of dynamical universality classes in open quantum systems, as well as identifying new protocols for quantum error correction.https://quantum-journal.org/papers/q-2025-01-28-1612/pdf/
spellingShingle Jinkang Guo
Oliver Hart
Chi-Fang Chen
Aaron J. Friedman
Andrew Lucas
Designing open quantum systems with known steady states: Davies generators and beyond
Quantum
title Designing open quantum systems with known steady states: Davies generators and beyond
title_full Designing open quantum systems with known steady states: Davies generators and beyond
title_fullStr Designing open quantum systems with known steady states: Davies generators and beyond
title_full_unstemmed Designing open quantum systems with known steady states: Davies generators and beyond
title_short Designing open quantum systems with known steady states: Davies generators and beyond
title_sort designing open quantum systems with known steady states davies generators and beyond
url https://quantum-journal.org/papers/q-2025-01-28-1612/pdf/
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AT chifangchen designingopenquantumsystemswithknownsteadystatesdaviesgeneratorsandbeyond
AT aaronjfriedman designingopenquantumsystemswithknownsteadystatesdaviesgeneratorsandbeyond
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